2003/06/12 by Andrzej Borowiec, Wieslaw A. Dudek, Steven Duplij
Mathematics · Physics and Astronomy · #math.QA #hep-th #math-ph #math.GR #math.MP #math.RA
published as Journal of Kharkov National University, ser. Nuclei, Particles and Fields, v. 529, N 3(15) (2001) pp. 21--29 · 11 pages, AmSLaTeX
arxiv created 2003/06/12 · arxiv updated 2009/11/30
The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bialgebras and Hopf algebras and investigate their properties. The main property "to be binary derived" is considered in detail. The co-analog of Post theorem is formulated. It is shown that there exist 3 types of ternary coassociativity, 3 types of ternary counits and 2 types of ternary antipodes. Some examples are also presented.